What does "SP" mean in model theory, as in "For a pair of cardinals ($\lambda$ ,$\kappa$) $\in SP(T)$ ..."?

Question

On page 27 of the model theory paper "A Primer on Simple Theories" (PDF), there is a notation "$SP(T)$" which is defined as follows:

For a pair of cardinals ($\lambda$ ,$\kappa$) $\in$ SP(T) if every model of cardinality $\lambda$ has a $\kappa$ saturated elementary extension of the same cardinality.

I'm looking for the word that "$SP$" stands for.

Answer 1

Shelah, S. (1980). Simple unstable theories. Annals of Mathematical Logic, 19(3), 177–203. https://doi.org/10.1016/0003-4843(80)90009-1 page 189

$SP(T)$ - saturation pairs of $T$

Answer 2

I believe that this notation originates in the paper Simple Unstable Theories (I could not find it in the index of abbreviations in Classification Theory). In that paper, Shelah writes:

Let $\mathrm{SP}_T(\lambda, \kappa)$ mean any model of $T$ of power $\lambda$ can be extended to a $\kappa$-saturated model of cardinality $\lambda$.

So it's reasonable to think that the S and P stand for "saturated" and "power" (here, "power" is being used a synonym for "cardinality" - I note with amusement that Shelah uses both words in the same sentence!).

Of course, this is just a guess. You could get a definitive answer by asking Shelah.

Edit: ...or by just reading the paper more carefully! Thanks to HasseWeyl for unearthing the correct answer: $\mathrm{SP}(T)$ means "Saturation pairs of $T$".